Tire non-uniformity relates to the symmetry (or lack of symmetry) relative to the tire's axis of rotation in certain quantifiable characteristics of a tire. Conventional tire building methods unfortunately have many opportunities for producing non-uniformities in tires. During rotation of the tires, non-uniformities present in the tire structure produce periodically-varying forces at the wheel axis. Tire non-uniformities are important when these force variations are transmitted as noticeable vibrations to the vehicle and vehicle occupants. These forces are transmitted through the suspension of the vehicle and may be felt in the seats and steering wheel of the vehicle or transmitted as noise in the passenger compartment. The amount of vibration transmitted to the vehicle occupants has been categorized as the “ride comfort” or “comfort” of the tires.
Tire uniformity parameters, or attributes, are generally categorized as dimensional or geometric variations (radial run out and lateral run out), mass variance, and rolling force variations (radial force variation, lateral force variation and tangential force variation, sometimes also called longitudinal or fore and aft force variation). Uniformity measurement machines often calculate the above and other uniformity characteristics by measuring force at a number of points around a tire as the tire is rotated about its axis to generate a uniformity waveform.
A measured uniformity waveform for a tire can result from uniformity dispersions due to both tire effects as well as process effects. Examples of tire effects include those due to tire material components (e.g., the product start point or joint overlap location of one or more of casing textile plies, belt plies, bead rings, inner liner, tread and other rubber layers of the tires), manufacturing techniques (e.g., the relative location in which a green tire is introduced on a building drum, placed into a mold or curing press, and the like), and/or controllable conditions used in the tire construction process (e.g., the temperature and pressure at which green tires are subjected during the curing process or other manufacturing steps.) Examples of process effects may arise from such manufacturing conditions as a roller influence, extruder surge, fluctuation in a process condition (e.g., temperature, pressure, speed, etc.) and others. The impact of tire effects and process effects within a measured uniformity waveform are respectively represented by “tire harmonic” or “process harmonic” components of the composite uniformity waveform.
The respective tire harmonics obtained from a measured uniformity waveform can be analyzed in accordance with known processes to improve tire uniformity. However, this analysis can be hindered by the impact of process effects whose periodic contributions to the composite uniformity waveform are not identical to the tire harmonics, resulting in poorer compensations and adjustments. Identification of such process harmonic uniformity contributions can help improve uniformity analysis as well as the tire building process.
Techniques are known to estimate the magnitude of process effect contributions. For example, one technique provides for the construction of rectangular coefficient coordinates associated with sine and cosine terms for each of a plurality of candidate process harmonics for a measured uniformity waveform for a tire. The rectangular coordinates can be solved for using, for instance, a regression analysis, and used to estimate the magnitude of each process harmonic. Since the rectangular coordinates are associated with both sine and cosine terms, the coordinates will be functions of both magnitude and phase angle (i.e. azimuthal location of the peak on the tire) of the process harmonics.
In certain cases, however, the phase angle may not be available or is otherwise desired not to be used. For instance, determination of the phase angle may require that a barcode or other indicator is attached to the tire during its manufacture to act as a reference point for measurement of the uniformity waveform. If this capability is absent from the manufacturing equipment, then the phase angle cannot be determined In other instances, the phase angle may never have been computed or stored in a memory for future use. In these cases, the above-mentioned analysis techniques may not be able to estimate process harmonic magnitudes.
Thus, a need exists for a system and method for estimating magnitudes of process harmonic contributions without relying on phase angle information for the candidate process harmonics.